2020/01/06 by Alfred Geroldinger, Qinghai Zhong · 2 citations
Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Rings, Modules, and Algebras
paper · pdf · doi:10.1007/s00233-019-10079-0
crossref issued 2020/01/06 · crossref published 2020/01/06 · crossref published-online 2020/01/06 · openalex publication_date 2020/01/06 · crossref created 2020/01/06 · crossref published-print 2020/02/01 · crossref deposited 2023/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03 · crossref indexed 2026/08/03
Abstract This is a survey on factorization theory. We discuss finitely generated monoids (including affine monoids), primary monoids (including numerical monoids), power sets with set addition, Krull monoids and their various generalizations, and the multiplicative monoids of domains (including Krull domains, rings of integer-valued polynomials, orders in algebraic number fields) and of their ideals. We offer examples for all these classes of monoids and discuss their main arithmetical finiteness properties. These describe the structure of their sets of lengths, of the unions of sets of lengths, and their catenary degrees. We also provide examples where these finiteness properties do not hold.